00020001010008main.ACT0002020011Trig_shifting.EAC010000002de7 Trig_shifting.EAC main.ACT!$.15H `E ')[4IAbout the graphs of a*sin(x), cos  a*x) and  irclesQ\Y AuthorplProfessor Wei-Chi Yang e-l: wyang@radford.edu @!URL: http://www.#/5E Objectives:[V/We would like to motivate the understandings ofgraph y=a*sin(x), cos Cy=a*x) C. by u9 g approprircircles, periods.[K[] Example 1l =. Explorev withr.\%C1.6EΈ  Q@hr `f6EqQr sw R Dv B7 A kL'C u xy   H  A 1.6sin(x)`H"#cos##F(as` "!F1 2FpDBb0$Sew0 fd8@<wQ (XRP Dellw!Gl2xl C%UATAf slWwls$6l1hl8l82SblTC`pTh%leuW@v  P4R#$Q`0g! <2FpHC&x0TT4 `1eAAlGvHrlcVlyc6l pgl wl(10l(  VeI f' CUpu av" 9#1gtDU iSh(X4(Y9VveI`%8V@d4#gd %(US!'euPb (te(te YPb 'euUS!  %00`#g< 8V@d`I`%<$Vve0Y9p<X4<Sh(HDU iP`1gt 9#` av"CUpuYfVeI@؈6:H" ((as "!F1V 2F DBbz Sew: fd8z wQ (XRDeulw!G2x. C%UA^Af s@Ww s$6P1h#$8`0"!F1<82SbpHTC`0TpTh%`euWlvl l4RlQlg! 2FlC&xlT4 l1eAAGvHrcVyc6 pg wl(10؆(*((4WBQvX,Ag)d'B(X@ 5  EyB@ $D%PAdY Yg6x0 `%`vp 5# Gg2$U50YHiT $01 0.1611073156 987050262 16041128099 322214631TL 948536441& 166679938_ 4833219467 885456025 0.464723172^Y4293Y4427634 6007422649805577 6927243535 721202447_94389_568064722983865 1.127751209 0.4286925614 9034504346& 1.2888585258 278217463K 9605181118 1.4499658\ 1205366803 9927088741o61107315-0.0402659401':9188998277218047L :20009389 0.979790658 933287787r3546048 0.935016242& 2.09439510$86602540z 2.2555024163244537]7Y0496' 2.416609734 -0.7485102 0.66312265 2.5777170499 845190085595344761973882436%r 9199794437r36` 2.89993168 970941817q23$56643 3.06103=6 996757308 0.0804665687:22214:1; 3.38325362Ҩl5409  -0.3919666099 3.705468258 & 8451900855 5344658261: 866575574: 7485107482N663122<:4.027s88` 6324453756 774604961:18879020Ԗ0254031 4.3498975 04887} 9350162425110048320002569^M9796`6721121r 0402659401=e9991983321946 0.1366803 -0.9927088741 44326783 0.2782174639%9 6051811169 5.1554340989 428692561490345043493165414&r 5680647467r 822983865r47764872o72435359 721202447҆63875604&9 799442763 60074226429 5'8633 885456025 423177.970678 948536441T663B 6.12207 0.9870502626 -0.1604112809 6.283185307&1.0[7@Highlt the matrix above and drag io stat eidtor below:\;Check out how we geSgraph of y=sin(2*t)Zy=cosԈN*4FinaForm$NGraph2D 3 LISTCAL(SYS4P Modify dPSTA<CixG<U\Sequence,SheetO|PolveEq^wrЈ(Upܒ tupFLG1܊<Lis{DPicTViewWindx_osvev&xy^ H2h (4<  Hy5 gV$( 0<_T`lx̆؆ !"H # J%  &3,7'8(D)P*\+ hnt -.01234Ȇ5ԆEFHI| J K L( M^NB@OLXQdRpS|T] ^_`ja bh<i,"0j@$ kT'8j)|)Ȇ͑)Ԇ Α)}  ) ׆SWؐ(* ِ<* ڐP* kېd*(d FinancialFormat  mqE $ list1/2 system]^_` a bFR @R@@x "!F1 2FpDBb0$.Sew0 fd8@<wQ (XRP Delw!G).2x p'2 C %UAAf s@$Ww0s$6P<1hGr8`T`'82SblTC`0xpTh%leuWlv 4RQ g!2FC&xlT4 1eAAGvHr cV(yc60 pg8# w,(10D(J $0<HT`lx̆؆& ,8DP\qh-t1 $Ԇ A b`  HSdAE`%p"D'c@.rCSP:hGF$(i%ax!tcH Sf0$evYVYT`HY$ 2DSuYHQH 0EY C pusl $WutUscatter% ^Ain StatGraph2. **In or wordscfor? is 2/2.[X13ꆬ#3vY-If we plot list4 (x) agains3,!get y=sin(2t),2ut the scatterBof # in StatGraph4.[[! Exercise 1.2G Co{rucq 3.5*cos(3ndwith appropriate circle*periody2yIy2.3yx/2z{ Remark: 2(1) TI forDa* is 2/a,F1((2) The amplitude for a*sin(x) and a*cos is a.eAct020012eActivity Save.EAC010000002de7 Trig_shifting.EAC main.ACT!$.15H `E ')[4IAbout the graphs of a*sin(x), cos  a*x) and  irclesQ\Y AuthorplProfessor Wei-Chi Yang e-l: wyang@radford.edu @!URL: http://www.#/5E Objectives:[V/We would like to motivate the understandings ofgraph y=a*sin(x), cos Cy=a*x) C. by u9 g approprircircles, periods.[K[] Example 1l =. Explorev withr.\%C1.6EΈ  Q@hr `f6EqQr sw R Dv B7 A kL'C u xy   H  A 1.6sin(x)`H"#cos##F(as` "!F1 2FpDBb0$Sew0 fd8@<wQ (XRP Dellw!Gl2xl C%UATAf slWwls$6l1hl8l82SblTC`pTh%leuW@v  P4R#$Q`0g! <2FpHC&x0TT4 `1eAAlGvHrlcVlyc6l pgl wl(10l(  VeI f' CUpu av" 9#1gtDU iSh(X4(Y9VveI`%8V@d4#gd %(US!'euPb (te(te YPb 'euUS!  %00`#g< 8V@d`I`%<$Vve0Y9p<X4<Sh(HDU iP`1gt 9#` av"CUpuYfVeI@؈6:H" ((as "!F1V 2F DBbz Sew: fd8z wQ (XRDeulw!G2x. C%UA^Af s@Ww s$6P1h#$8`0"!F1<82SbpHTC`0TpTh%`euWlvl l4RlQlg! 2FlC&xlT4 l1eAAGvHrcVyc6 pg wl(10؆(*((4WBQvX,Ag)d'B(X@ 5  EyB@ $D%PAdY Yg6x0 `%`vp 5# Gg2$U50YHiT $01 0.1611073156 987050262 16041128099 322214631TL 948536441& 166679938_ 4833219467 885456025 0.464723172^Y4293Y4427634 6007422649805577 6927243535 721202447_94389_568064722983865 1.127751209 0.4286925614 9034504346& 1.2888585258 278217463K 9605181118 1.4499658\ 1205366803 9927088741o61107315-0.0402659401':9188998277218047L :20009389 0.979790658 933287787r3546048 0.935016242& 2.09439510$86602540z 2.2555024163244537]7Y0496' 2.416609734 -0.7485102 0.66312265 2.5777170499 845190085595344761973882436%r 9199794437r36` 2.89993168 970941817q23$56643 3.06103=6 996757308 0.0804665687:22214:1; 3.38325362Ҩl5409  -0.3919666099 3.705468258 & 8451900855 5344658261: 866575574: 7485107482N663122<:4.027s88` 6324453756 774604961:18879020Ԗ0254031 4.3498975 04887} 9350162425110048320002569^M9796`6721121r 0402659401=e9991983321946 0.1366803 -0.9927088741 44326783 0.2782174639%9 6051811169 5.1554340989 428692561490345043493165414&r 5680647467r 822983865r47764872o72435359 721202447҆63875604&9 799442763 60074226429 5'8633 885456025 423177.970678 948536441T663B 6.12207 0.9870502626 -0.1604112809 6.283185307&1.0[7@Highlt the matrix above and drag io stat eidtor below:\;Check out how we geSgraph of y=sin(2*t)Zy=cosԈN*4FinaForm$NGraph2D 3 LISTCAL(SYS4P Modify dPSTA<CixG<U\Sequence,SheetO|PolveEq^wrЈ(Upܒ tupFLG1܊<Lis{DPicTViewWindx_osvev&xy^ H2h (4<  Hy5 gV$( 0<_T`lx̆؆ !"H # J%  &3,7'8(D)P*\+ hnt -.01234Ȇ5ԆEFHI| J K L( M^NB@OLXQdRpS|T] ^_`ja bh<i,"0j@$ kT'8j)|)Ȇ͑)Ԇ Α)}  ) ׆SWؐ(* ِ<* ڐP* kېd*(d FinancialFormat  mqE $ list1/2 system]^_` a bFR @R@@x "!F1 2FpDBb0$.Sew0 fd8@<wQ (XRP Delw!G).2x p'2 C %UAAf s@$Ww0s$6P<1hGr8`T`'82SblTC`0xpTh%leuWlv 4RQ g!2FC&xlT4 1eAAGvHr cV(yc60 pg8# w,(10D(J $0<HT`lx̆؆& ,8DP\qh-t1 $Ԇ A b`  HSdAE`%p"D'c@.rCSP:hGF$(i%ax!tcH Sf0$evYVYT`HY$ 2DSuYHQH 0EY C pusl $WutUscatter% ^Ain StatGraph2. **In or wordscfor? is 2/2.[X13ꆬ#3vY-If we plot list4 (x) agains3,!get y=sin(2t),2ut the scatterBof # in StatGraph4.[[! 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